Abstract
The ruin probability of an insurance company paying dividends according to a barrier strategy with a step barrier function is considered. Upper bounds for the probability of ruin are obtained within the framework of Sparre Andersen and Cramer–Lundberg risk models.
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References
E. Sparre Andersen, “On the Collective Theory of Risk in Case of Contagion Between the Claims,” in Trans. XVth Int. Congress Actuaries. Vol. II (N.Y., 1957), pp. 219–229.
V. V. Kalashnikov and D. G. Konstantinidis, “Probability of ruin,” Fund. Prikl. Matem. 2 (4), 1055 (1996).
H. Schmidli, Stochastic Control in Insurance (Springer-Verlag, L., 2008).
H. Albrecher, J. Hartinger, and S. Thonhauser, “On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model,” ASTIN Bull. 37 (2), 203 (2007).
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Original Russian Text © A.A. Muromskaya, 2017, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2017, Vol. 72, No. 1, pp. 32–36.
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Muromskaya, A.A. Generalization of Lundberg’s inequality for the case of stock insurance company. Moscow Univ. Math. Bull. 72, 31–34 (2017). https://doi.org/10.3103/S0027132217010053
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DOI: https://doi.org/10.3103/S0027132217010053